When Gordon Hayward's final three-point attempt proved (barely) errant, it not only won Mike Krzyzewski his fourth NCAA championship at Duke, it also saved him from what would have surely been one of the most second-guessed decisions in basketball history. Immediately prior to Hayward's shot, Krzyzewski asked center Brian Zoubek to intentionally miss his second free throw with the Blue Devils leading by two points. After the game, the Basketball Prospectus team discussed the decision via e-mail.

Kevin Pelton: My initial thought was it would be pretty difficult to justify the miss, but I put together a spreadsheet to play with some numbers. Essentially there are three scenarios:

1. Intentionally miss
2. Attempt FT; make
3. Attempt FT; miss

1 and 3 seem identical at worst, but according to the postgame quotes part of Duke's logic was they wanted Zoubek to be able to pressure Hayward, which presumably would have been more difficult if he was actually trying to make the shot.

Assuming you think the game is 50-50 in overtime (and Ken's computer would disagree), the amount Butler's chances of hitting the heave generally have to increase by 2 + 3 combined have to be larger than the odds of them hitting the heave in 1 to make intentionally missing make sense.

So, for example, I started with a 5% chance of hitting after an intentional miss. If you say they would have had a 10% chance of hitting the heave after a make and even 6% after an unintentional miss, it makes sense to foul. I still think that overstates how much value you gain from the intentional miss, but it's not unjustifiable at that level.

I'm curious to hear other people's opinions, however.

Bradford Doolittle: The bottom line to me is that a make in that situation means that a heave ties the game. Either way it was going to take a miraculous shot. I'd rather overtime be my worst-case scenario.

Ken Pomeroy: I guess the difference between losing on a half-court heave and losing in OT after a half-court heave ties it is pretty small. The decision is largely dependent on how much of a difference starting the possession without an inbounds makes. With one second left it's a great decision. With five, it's debatable. I am just surprised that after not seeing that move made very often at all for years, it's now the obvious thing to do.

Bradford: To echo what Ken said, the time element is crucial. I don't know what the cut-off is, but the fact that Hayward was able to cleanly grab the rebound and dribble to half court for a reasonably good look tells me there was too much time left for an intentional miss. This is more a gut reaction than an evaluation of the probabilities.

Discussions of end-of-game scenarios are quite relevant right now because the book on these strategies seems to be in flux among coaches at both levels more than ever.

Kevin: The best breakdown of this I saw was Wayne Winston's, which simplifies things a little (it might be fair to throw out how much Zoubek being able to defend on an intentional miss helps by counterbalancing it with the slim chance of Duke getting an offensive rebound, which I didn't consider) but comes to a similar conclusion. Basically, the chances of hitting a half-court shot have to double on a make to justify the decision. That's where you can debate it, since nobody has those numbers handy that I know of.

At the very least, it looks like there was wiggle room for Krzyzewski to defend his decision either way.